Acomputer consulting firm presently has bids out on three projects. let ai = {awarded project i}, for i = 1, 2, 3, and suppose that p(a1) = 0.22, p(a2) = 0.25, p(a3) = 0.28, p(a1 ∩ a2) = 0.12, p(a1 ∩ a3) = 0.03, p(a2 ∩ a3) = 0.06, p(a1 ∩ a2 ∩ a3) = 0.01. express in words each of the following events, and compute the probability of each event. (a) a1 ∪ a2

(a) P(A1 ∪ A2) = 0.35

Step-by-step explanation:

(a) A1 ∪ A2 :

We start by defining the events.

A1 : '' awarded project 1''

A2 : ''awarded project 2''

A3: ''awarded project 3''

In set theory we write the union of events A and B as A∪B.

A∪B means that the event A occurs,event B occurs or either both events occurs at the same time.

The probability is given by the equation :

P(A∪B) = P(A) + P(B) - P(A∩B) (1)

Where the event (A∩B) is the event where A and B occur at the same time

and P(A∩B) is the probability of (A∩B)

Using the equation (1) :

P(A1 ∪ A2) = P(A1) + P(A2) - P(A1∩A2)

P(A1 ∪ A2) = 0.22 + 0.25 - 0.12

P(A1 ∪ A2) = 0.35

answer

explanation

the area of a circle is calculated using the formula

or

we can use any of the above formulae to calculate the required. preferably, let us use the latter since the diameter is

we substitute the diameter into the formula to get:

this is the exact value for the area of the circle.

the correct answer is a

d

step-by-step explanation: